Repulsive Casimir Force from Fractional Neumann Boundary Conditions

TL;DR

This paper investigates how fractional Neumann boundary conditions influence the finite temperature Casimir force in a rectangular cavity, revealing conditions under which the force is attractive or repulsive.

Contribution

It introduces fractional Neumann boundary conditions to interpolate between Dirichlet and Neumann cases, analyzing their effect on the Casimir force at finite temperature.

Findings

For fractional order > 1/2, the Casimir force is always repulsive.

For fractional orders near 1/2, the force can be attractive or repulsive depending on cavity aspect ratio and temperature.

The fractional order controls the transition between attractive and repulsive Casimir forces.

Abstract

This paper studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a $d$-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.